On the cohomology of generalized triangle groups

  • Graham Ellis

    National University of Ireland, Galway, Ireland
  • Gerald Williams

    University of Kent at Canterbury, UK


We describe a general approach to constructing small free ZΓ{\Bbb Z}\Gamma-resolutions for certain infinite isometry groups Γ\Gamma. We apply the method to a class of generalized triangle groups and use the resolution to compute the integral homology of these groups. In illustrating the method we also obtain resolutions for the classical triangle groups and for their infinite cyclic central extensions, considered previously by Strebel.

Cite this article

Graham Ellis, Gerald Williams, On the cohomology of generalized triangle groups. Comment. Math. Helv. 80 (2005), no. 3, pp. 571–591

DOI 10.4171/CMH/26